Calculate the mle estimate for mean, Applied Statistics

Assignment Help:

Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They received the following scores: 400, 450, 575, 600, and 625.

(a) Assuming a normal distribution, write out the likelihood function for estimating the mean μ and standard deviation σ of the average class score.

(b) Calculate the MLE estimate for μ and the standard deviation (σ) for this class.

(c) What is the value of the log-likelihood function at this estimate?

(d) What is the least-squares estimate for μ and σ in your data? Are there any differences? Why or why not?

(e) Using a likelihood-ratio test, test whether the MLE estimates from the class are significantly different from the national mean of 500 and national standard deviation of 100.

(Hint: Start by plugging those values into your log-likelihood function. Remember you are testing two restrictions).


Related Discussions:- Calculate the mle estimate for mean

Theoretical yield and actual yield, Write down the symbols and unit for the...

Write down the symbols and unit for the following: mass, molar mass, molar and molarity Write down the relationship between mass and molar mass and show that the units match.

Inference on reggression analysis, find the expected value of the mean squa...

find the expected value of the mean square error and of the mean square reggression

Econometrics, Ask question From the household budget survey of 1980 of the...

Ask question From the household budget survey of 1980 of the Dutch Central Bureau of Statistics, J. S. Cramer obtained the following logit model based on a sample of 2820 househol

Multiple regression analysis, Complete the multiple regression model using ...

Complete the multiple regression model using Y and your combined X variables.  State the equation.  Next, make sure that you evaluate overall model performance with the Anova table

Define the term multicollinearity, Question: (a) (i) Define the term ...

Question: (a) (i) Define the term multicollinearity. (ii) Explain why it is important to guard against multicollinearity. (b) (i) Sometimes we encounter missing values

Classical and modern regression, The data in the data frame asset are from ...

The data in the data frame asset are from Myers (1990), \Classical and Modern Regression with Applications (Second Edition)," Duxbury. The response y here is rm return on assets f

Chi-square analysis, Chi-square analysis can be used with both Goodness-of-...

Chi-square analysis can be used with both Goodness-of-Fit Tests and with Tests for Independence. There are specific instances when each test should be used based on the information

Evaluate the p - value, Use the given information to find the P-value. T...

Use the given information to find the P-value. The test statistic in a two-tailed test is z = 1.49 P-value = (round to four decimal places as needed)

Appropriate statistical test, I would like to know what the appropriate sta...

I would like to know what the appropriate statistical test is for investigating an association between a nominal variable and an ordinal variable assuming normal distribution? It''

Financial payments technology, Suppose the money supply process is now repr...

Suppose the money supply process is now represented by the following function: where m measures the sensitivity of money supply with respect to the interest rate. (i) Us

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd